Topologies on closed and closed convex sets. Mathematics and its applications Reidel 268; Mathematics and its applications 268.

Beer, Gerald:

ISBN 10: 0792325311 / ISBN 13: 9780792325314

Editore: Dordrecht Boston , Kluwer Academic Publishers [1993]., 1993

Riguardo questo articolo

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 54 BEE 9780792325314 Sprache: Englisch Gewicht in Gramm: 550.

Codice articolo 2498362

Dati bibliografici

• Titolo: Topologies on closed and closed convex sets. Mathematics and its applications Reidel 268; Mathematics and its applications 268.
• Editore: Dordrecht Boston , Kluwer Academic Publishers [1993].
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0792325311
• ISBN 13: 9780792325314
• Rilegatura: Hardcover
• Cataloghi dei venditori:
  • SA MATHEMATIK

Descrizione articolo

Riassunto

This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text.
This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.

Contenuti

Preface. 1. Preliminaries. 2. Weak Topologies determined by Distance Functionals. 3. The Attouch--Wets and Hausdorff Metric Topologies. 4. Gap and Excess Functionals and Weak Topologies. 5. The Fell Topology and Kuratowski--Painlevé Convergence. 6. Multifunctions - the Rudiments. 7. The Attouch--Wets Topology for Convex Functions. 8. The Slice Topology for Convex Functions. Notes and References. Bibliography. Symbols and Notation. Subject Index.